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Legendre's three-square theorem

In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers

if and only if n is not of the form for integers a and b.

The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as ) are

History

Pierre de Fermat gave a criterion for numbers of the form 3a+1 to be a sum of 3 squares essentially equivalent to Legendre's theorem, but did not provide a proof. N. Beguelin noticed in 1774 that every positive integer which is neither of the form 8n + 7, nor of the form 4n, is the sum of three squares, but did not provide a satisfactory proof. In 1796 Gauss proved his Eureka theorem that every positive integer n is the sum of 3 triangular numbers; this is trivially equivalent to the fact that 8n+3 is a sum of 3 squares. In 1797 or 1798 A.-M. Legendre obtained the first proof of his 3 square theorem. In 1813, A. L. Cauchy noted that Legendre's theorem is equivalent to the statement in the introduction above. Previously, in 1801, C. F. Gauss had obtained a more general result, containing Legendre theorem of 1797-8 as a corollary. In particular, Gauss counted the number of solutions of the expression of an integer as a sum of three squares, and this is a generalisation of yet another result of Legendre, whose proof is incomplete. This last fact appears to be the reason for later incorrect claims according to which Legendre's proof of the three-square theorem was defective and had to be completed by Gauss.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Legendre's_three-square_theorem

Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.

Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Theorem

Teorema (film)

Teorema is a 1968 Italian art-house film written and directed by Pier Paolo Pasolini and starring Terence Stamp, Laura Betti, Silvana Mangano, Massimo Girotti, and Anne Wiazemsky. It was the first time Pasolini worked primarily with professional actors. In this film, an upper-class Milanese family is introduced to, and then abandoned by, a divine force. Two prevalent motifs are the desert and the timelessness of divinity.

Plot

A mysterious figure known only as "The Visitor" appears in the lives of a typical bourgeois Italian family. His arrival is heralded at the gates of the family's Milanese estate by an arm-flapping postman. The enigmatic stranger soon engages in sexual affairs with all members of the household: the devoutly religious maid, the sensitive son, the sexually repressed mother, the timid daughter and, finally, the tormented father. The stranger gives unstintingly of himself, asking nothing in return. He stops the passionate maid from committing suicide with a gas hose and tenderly consoles her; he befriends and sleeps with the frightened son, soothing his doubts and anxiety and endowing him with confidence; he becomes emotionally intimate with the overprotected daughter, removing her childish innocence about men; he seduces the bored and dissatisfied mother, giving her sexual joy and fulfillment; he cares for and comforts the despondent and suffering father, who has fallen ill.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Teorema_(film)

Dynkin system

A Dynkin system, named after Eugene Dynkin, is a collection of subsets of another universal set satisfying a set of axioms weaker than those of σ-algebra. Dynkin systems are sometimes referred to as λ-systems (Dynkin himself used this term) or d-system. These set families have applications in measure theory and probability.

The primary relevance of λ-systems are their use in applications of the π-λ theorem.

Definitions

Let Ω be a nonempty set, and let be a collection of subsets of Ω (i.e., is a subset of the power set of Ω). Then is a Dynkin system if

Ω ∈ ,

if A, B ∈ and A ⊆ B, then B \ A ∈ ,

if A₁, A₂, A₃, ... is a sequence of subsets in and A_n ⊆ A_n+1 for all n ≥ 1, then .

Equivalently, is a Dynkin system if

Ω ∈ ,

if A ∈ D, then A^c ∈ D,

if A₁, A₂, A₃, ... is a sequence of subsets in such that A_i ∩ A_j = Ø for all i ≠ j, then .

The second definition is generally preferred as it usually is easier to check.

An important fact is that a Dynkin system which is also a π-system (i.e., closed under finite intersection) is a σ-algebra. This can be verified by noting that condition 3 and closure under finite intersection implies closure under countable unions.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Dynkin_system

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  Bayes theorem, the geometry of changing beliefs

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15:11

Bayes theorem, the geometry of changing beliefs

• Order: Reorder
• Duration: 15:11
• Uploaded Date: 22 Dec 2019
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Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simp...

Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/ The study with Steve: https://science.sciencemag.org/content/185/4157/1124 http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. Contents: 0:00 - Intro example 4:09 - Generalizing as a formula 10:13 - Making probability intuitive 13:35 - Issues with the Steve example Thanks to these viewers for their contributions to translations Gujarati: Hitesh12358, Pragna1991 Hebrew: Omer Tuchfeld Italian: @crampaldo ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

https://wn.com/Bayes_Theorem,_The_Geometry_Of_Changing_Beliefs

Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/ The study with Steve: https://science.sciencemag.org/content/185/4157/1124 http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. Contents: 0:00 - Intro example 4:09 - Generalizing as a formula 10:13 - Making probability intuitive 13:35 - Issues with the Steve example Thanks to these viewers for their contributions to translations Gujarati: Hitesh12358, Pragna1991 Hebrew: Omer Tuchfeld Italian: @crampaldo ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

• published: 22 Dec 2019
• views: 4555622

1:27

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI

• Order: Reorder
• Duration: 1:27
• Uploaded Date: 11 Mar 2013
• views: 554986

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI. Subscribe: http://bit.ly/subscribetotheBFI Pier Paolo Pasolini's playful satire, starring Terence Stamp...

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI. Subscribe: http://bit.ly/subscribetotheBFI Pier Paolo Pasolini's playful satire, starring Terence Stamp at the peak of his beauty. In cinemas 12 April Book tickets: http://bit.ly/13P9ula Watch more on the BFI Player: http://player.bfi.org.uk/ Follow us on Twitter: https://twitter.com/BFI Like us on Facebook: https://www.facebook.com/BritishFilmInstitute Follow us on Google+: https://plus.google.com/+britishfilminstitute/

https://wn.com/Theorem_(1968)_Pier_Paolo_Pasolini_(Trailer)_|_Bfi

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI. Subscribe: http://bit.ly/subscribetotheBFI Pier Paolo Pasolini's playful satire, starring Terence Stamp at the peak of his beauty. In cinemas 12 April Book tickets: http://bit.ly/13P9ula Watch more on the BFI Player: http://player.bfi.org.uk/ Follow us on Twitter: https://twitter.com/BFI Like us on Facebook: https://www.facebook.com/BritishFilmInstitute Follow us on Google+: https://plus.google.com/+britishfilminstitute/

• published: 11 Mar 2013
• views: 554986

4:39

An introduction to mathematical theorems - Scott Kennedy

• Order: Reorder
• Duration: 4:39
• Uploaded Date: 10 Sep 2012
• views: 497457

View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics ...

View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally convincing proof. Lesson by Scott Kennedy, animation by Karrot Animation.

https://wn.com/An_Introduction_To_Mathematical_Theorems_Scott_Kennedy

View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally convincing proof. Lesson by Scott Kennedy, animation by Karrot Animation.

• published: 10 Sep 2012
• views: 497457

4:11

Everything About Circle Theorems - In 3 minutes!

• Order: Reorder
• Duration: 4:11
• Uploaded Date: 20 May 2015
• views: 2895259

This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to unde...

This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to understand it myself, once i got to grips with it i decided to help others who were also stuck.. so this video was created... This video includes Perpendicular bisectors of any chord the angles in a semi-circle, what happens when a tangent and a radius meet, Angles that are in the same segment and how different they are, the circumference subtended by the same arc, the meaning of subtended, lengths of two tangents and finally the angle between a tangent and a chord.. aka Alternate Segment Theorem. I re-uploaded this video because the last one had some glitches so here we are againn.... FOR THE QUESTION IF YOU ARE STUCK okay so angle A is 55degrees. this is because the whole isosceles triangle adds up to 180degrees, you now take 70degrees from this because the angle on the far right hand side is 70degrees. this leaves us with 110degrees and you divide it by two (due to it being isosceles triangle) so angle A is 55degrees. if you go to 1:07 this explains the next part on why there is a 90degree angle on top of angle B.  you take 55degrees from that 90degrees because part of the right angle overlaps the first isosceles triangle (on the right hand side) and we have previously worked out that, that angle is 55degrees, this leaves us with 35degrees. now times that 35 by 2 which gives you 70degrees, take that answer AWAY from 180degrees because as you can see angle D is within ANOTHER isosceles triangle which means all the angles within the triangle add up to 180degrees. because angle D is within that triangle, angle D and the angle at the bottom right of the Isosceles triangle will EQUAL to the same amount. now divide the 110degrees by 2 to give you 55degrees.

https://wn.com/Everything_About_Circle_Theorems_In_3_Minutes

This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to understand it myself, once i got to grips with it i decided to help others who were also stuck.. so this video was created... This video includes Perpendicular bisectors of any chord the angles in a semi-circle, what happens when a tangent and a radius meet, Angles that are in the same segment and how different they are, the circumference subtended by the same arc, the meaning of subtended, lengths of two tangents and finally the angle between a tangent and a chord.. aka Alternate Segment Theorem. I re-uploaded this video because the last one had some glitches so here we are againn.... FOR THE QUESTION IF YOU ARE STUCK okay so angle A is 55degrees. this is because the whole isosceles triangle adds up to 180degrees, you now take 70degrees from this because the angle on the far right hand side is 70degrees. this leaves us with 110degrees and you divide it by two (due to it being isosceles triangle) so angle A is 55degrees. if you go to 1:07 this explains the next part on why there is a 90degree angle on top of angle B.  you take 55degrees from that 90degrees because part of the right angle overlaps the first isosceles triangle (on the right hand side) and we have previously worked out that, that angle is 55degrees, this leaves us with 35degrees. now times that 35 by 2 which gives you 70degrees, take that answer AWAY from 180degrees because as you can see angle D is within ANOTHER isosceles triangle which means all the angles within the triangle add up to 180degrees. because angle D is within that triangle, angle D and the angle at the bottom right of the Isosceles triangle will EQUAL to the same amount. now divide the 110degrees by 2 to give you 55degrees.

• published: 20 May 2015
• views: 2895259

5:20

The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

• Order: Reorder
• Duration: 5:20
• Uploaded Date: 20 Jul 2021
• views: 3814072

Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “...

Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Connect With Us ---------------------------------------------- Sign up for our newsletter: http://bit.ly/TEDEdNewsletter Follow us on Facebook: http://bit.ly/TEDEdFacebook Find us on Twitter: http://bit.ly/TEDEdTwitter Peep us on Instagram: http://bit.ly/TEDEdInstagram ---------------------------------------------- Keep Learning ---------------------------------------------- View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper Animator's website: https://basaestudio.com ---------------------------------------------- Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.

https://wn.com/The_Paradox_At_The_Heart_Of_Mathematics_Gödel's_Incompleteness_Theorem_Marcus_Du_Sautoy

Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Connect With Us ---------------------------------------------- Sign up for our newsletter: http://bit.ly/TEDEdNewsletter Follow us on Facebook: http://bit.ly/TEDEdFacebook Find us on Twitter: http://bit.ly/TEDEdTwitter Peep us on Instagram: http://bit.ly/TEDEdInstagram ---------------------------------------------- Keep Learning ---------------------------------------------- View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper Animator's website: https://basaestudio.com ---------------------------------------------- Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.

• published: 20 Jul 2021
• views: 3814072

0:44

Pythagorean theorem water demo

• Order: Reorder
• Duration: 0:44
• Uploaded Date: 14 Apr 2009
• views: 2795697

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

https://wn.com/Pythagorean_Theorem_Water_Demo

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

• published: 14 Apr 2009
• views: 2795697

5:50

Puscifer - "Theorem" (Official Video)

• Order: Reorder
• Duration: 5:50
• Uploaded Date: 02 Nov 2020
• views: 994558

Puscifer’s video for “Theorem,” from the album “Existential Reckoning” Listen to Puscifer: Apple Music – https://music.apple.com/us/artist/puscifer/48261730 ...

Puscifer’s video for “Theorem,” from the album “Existential Reckoning” Listen to Puscifer: Apple Music – https://music.apple.com/us/artist/puscifer/48261730 Spotify – https://open.spotify.com/artist/2pAajGWerK3ghwToNWFENS?si=DSiEUvpBS86Nzj54L_Bhvg Amazon Music - https://www.amazon.com/music/player/artists/B000TE0AUC Tidal - https://tidal.com/browse/artist/65016 Sign-up for tour updates: https://bnds.us/6qsj7t Watch more Puscifer videos: https://www.youtube.com/@pusciferdotcom/videos Subscribe to Puscifer’s YouTube channel: https://www.youtube.com/@pusciferdotcom?sub_confirmation=1 Follow Puscifer: Website & Store: https://puscifer.com/ Facebook: https://www.facebook.com/PusciferMusic Twitter: https://twitter.com/puscifer Instagram: https://www.instagram.com/puscifer/ YouTube: https://www.youtube.com/@pusciferdotcom Lyrics: Old notions: traps by nature, holding sentry over, we, the rigid, the self suppressing. New notions: holes we dig too quickly into which we fall. Just impulsive postulations. Seek the Balance. Work the Science. Through diligence, moderate the middle. Resilient, social architectures must be built upon arbitrated firm foundations. Integrating form & function, art & order, hope & proof, math & passion. Theorems old and new Seek the Balance. Work the Science. Be diligent. Moderate the middle. Synthesize. ©2020 Puscifer Entertainment under exclusive license to Alchemy Recordings, LLC / BMG Rights Management (US). FOLLOW ALCHEMY RECORDINGS https://www.facebook.com/AlchemyRecor... https://twitter.com/alchemyrecords https://www.instagram.com/alchemyreco... https://www.alchemyrecordings.com #Puscifer #Theorem #ExistentialReckoning

https://wn.com/Puscifer_Theorem_(Official_Video)

Puscifer’s video for “Theorem,” from the album “Existential Reckoning” Listen to Puscifer: Apple Music – https://music.apple.com/us/artist/puscifer/48261730 Spotify – https://open.spotify.com/artist/2pAajGWerK3ghwToNWFENS?si=DSiEUvpBS86Nzj54L_Bhvg Amazon Music - https://www.amazon.com/music/player/artists/B000TE0AUC Tidal - https://tidal.com/browse/artist/65016 Sign-up for tour updates: https://bnds.us/6qsj7t Watch more Puscifer videos: https://www.youtube.com/@pusciferdotcom/videos Subscribe to Puscifer’s YouTube channel: https://www.youtube.com/@pusciferdotcom?sub_confirmation=1 Follow Puscifer: Website & Store: https://puscifer.com/ Facebook: https://www.facebook.com/PusciferMusic Twitter: https://twitter.com/puscifer Instagram: https://www.instagram.com/puscifer/ YouTube: https://www.youtube.com/@pusciferdotcom Lyrics: Old notions: traps by nature, holding sentry over, we, the rigid, the self suppressing. New notions: holes we dig too quickly into which we fall. Just impulsive postulations. Seek the Balance. Work the Science. Through diligence, moderate the middle. Resilient, social architectures must be built upon arbitrated firm foundations. Integrating form & function, art & order, hope & proof, math & passion. Theorems old and new Seek the Balance. Work the Science. Be diligent. Moderate the middle. Synthesize. ©2020 Puscifer Entertainment under exclusive license to Alchemy Recordings, LLC / BMG Rights Management (US). FOLLOW ALCHEMY RECORDINGS https://www.facebook.com/AlchemyRecor... https://twitter.com/alchemyrecords https://www.instagram.com/alchemyreco... https://www.alchemyrecordings.com #Puscifer #Theorem #ExistentialReckoning

• published: 02 Nov 2020
• views: 994558

8:48

What Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz

• Order: Reorder
• Duration: 8:48
• Uploaded Date: 07 Aug 2020
• views: 668924

What Is Pythagoras Theorem? | Pythagoras Theorem Explained | Theorem For Kids | Maths For Kids | Maths Theorem | Hypotenuse | Best Kids Show | Dr Binocs Show | ...

What Is Pythagoras Theorem? | Pythagoras Theorem Explained | Theorem For Kids | Maths For Kids | Maths Theorem | Hypotenuse | Best Kids Show | Dr Binocs Show | Dr Binocs | Peekaboo Kidz Hey kids, in this video, Dr Binocs will explain, Why Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz Make sure you watch the whole video to know all the answers to your curious questions! Leave your ideas, suggestions and questions for Dr. Binocs at this Email Id: [email protected] For more fun learning videos SUBSCRIBE to Peekaboo Kidz: http://bit.ly/SubscribeTo-Peekabookidz Watch Guess The Shapes With Baby Binocs here - https://youtu.be/vNm422Ta44w Watch other fun learning episodes of Dr. Binocs here - http://bit.ly/2kfNS22 Watch our NEW SERIES of Baby Binocs, stay tuned to this playlist - http://bit.ly/2kyC2jU Credits - Voice of Dr. Binocs & Kitty - Joseph D'Souza Creative Head/Director - Nitin Navale Writer - Nitin Navale Illustrators - Kalpesh Bamne, Mukesh Ishi Storyboard - Kalpesh Bamne Animators - Sushant Hodage, Tushar Ishi , Raju Nikumbe, Prashant Bordekar Co-ordinator- Aliasgar Kagalwala VFX Artist - Tushar Ishi Original Background Score & SFX - Varad J. Khare Sound Design: Varad J. Khare Sound Engineer - Varad J. Khare Producer - Neha Barjatya Copyrights and Publishing: Rajshri Entertainment Private Limited All rights reserved. #WhatIsPythagorasTheorem #PythagorasTheorem #DrBinocsShow #PeekabooKidz Catch Dr.Binocs At - https://goo.gl/SXhLmc To Watch More Popular Nursery Rhymes Go To - https://goo.gl/CV0Xoo To Watch Alphabet Rhymes Go To - https://goo.gl/qmIRLv To Watch Compilations Go To - https://goo.gl/nW3kw9 Catch More Lyricals At - https://goo.gl/A7kEmO Subscribe to Peekaboo Kidz: http://bit.ly/peekabookidz Like our Facebook page: https://www.facebook.com/peekabootv

https://wn.com/What_Is_Pythagoras_Theorem_|_Pythagoras_Theorem_|_The_Dr_Binocs_Show_|_Peekaboo_Kidz

What Is Pythagoras Theorem? | Pythagoras Theorem Explained | Theorem For Kids | Maths For Kids | Maths Theorem | Hypotenuse | Best Kids Show | Dr Binocs Show | Dr Binocs | Peekaboo Kidz Hey kids, in this video, Dr Binocs will explain, Why Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz Make sure you watch the whole video to know all the answers to your curious questions! Leave your ideas, suggestions and questions for Dr. Binocs at this Email Id: [email protected] For more fun learning videos SUBSCRIBE to Peekaboo Kidz: http://bit.ly/SubscribeTo-Peekabookidz Watch Guess The Shapes With Baby Binocs here - https://youtu.be/vNm422Ta44w Watch other fun learning episodes of Dr. Binocs here - http://bit.ly/2kfNS22 Watch our NEW SERIES of Baby Binocs, stay tuned to this playlist - http://bit.ly/2kyC2jU Credits - Voice of Dr. Binocs & Kitty - Joseph D'Souza Creative Head/Director - Nitin Navale Writer - Nitin Navale Illustrators - Kalpesh Bamne, Mukesh Ishi Storyboard - Kalpesh Bamne Animators - Sushant Hodage, Tushar Ishi , Raju Nikumbe, Prashant Bordekar Co-ordinator- Aliasgar Kagalwala VFX Artist - Tushar Ishi Original Background Score & SFX - Varad J. Khare Sound Design: Varad J. Khare Sound Engineer - Varad J. Khare Producer - Neha Barjatya Copyrights and Publishing: Rajshri Entertainment Private Limited All rights reserved. #WhatIsPythagorasTheorem #PythagorasTheorem #DrBinocsShow #PeekabooKidz Catch Dr.Binocs At - https://goo.gl/SXhLmc To Watch More Popular Nursery Rhymes Go To - https://goo.gl/CV0Xoo To Watch Alphabet Rhymes Go To - https://goo.gl/qmIRLv To Watch Compilations Go To - https://goo.gl/nW3kw9 Catch More Lyricals At - https://goo.gl/A7kEmO Subscribe to Peekaboo Kidz: http://bit.ly/peekabookidz Like our Facebook page: https://www.facebook.com/peekabootv

• published: 07 Aug 2020
• views: 668924

11:04

Pythagorean Theorem

• Order: Reorder
• Duration: 11:04
• Uploaded Date: 29 Dec 2017
• views: 530987

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In a...

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhombuses, and trapezoids. This video explains how to calculate the perimeter of a rhombus and the area of a trapezoid using the pythagorean theorem as well as the side length of a square given the length of the diagonal. This geometry video contains plenty of examples and practice problems. Polygons: https://www.youtube.com/watch?v=E_-3ulbtcLk Quadrilaterals: https://www.youtube.com/watch?v=ogcH3eM5beM Points, Lines, Planes, & Segments: https://www.youtube.com/watch?v=dDWjhRfBsKM Similar Triangles: https://www.youtube.com/watch?v=YiFwvAFk-xs Pythagorean Theorem: https://www.youtube.com/watch?v=d8EA5TxGzcY _________________________________ The Distance Formula: https://www.youtube.com/watch?v=YDvUy5VYm9E Distance Between 2 Points - 3D: https://www.youtube.com/watch?v=0c6cP2zLC2c Special Right Triangles - 30 60 90: https://www.youtube.com/watch?v=p70UBGCHZrQ Special Right Triangles - 45 45 90: https://www.youtube.com/watch?v=xzMirNSv1d0 Trigonometric Ratios: https://www.youtube.com/watch?v=9-eHMMpQC2k _________________________________ Angle of Elevation Word Problems: https://www.youtube.com/watch?v=uyKvSe6Ltgs Finding The Missing Side of a triangle: https://www.youtube.com/watch?v=tielQ3ejh70 Finding The Missing Angle of a Triangle: https://www.youtube.com/watch?v=4Dv5IFqATrc Two Triangle Trigonometry Problems: https://www.youtube.com/watch?v=OTP885mApV8 How To Find The Area of a Rectangle: https://www.youtube.com/watch?v=M8JdRHeQBW8 ________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections

https://wn.com/Pythagorean_Theorem

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhombuses, and trapezoids. This video explains how to calculate the perimeter of a rhombus and the area of a trapezoid using the pythagorean theorem as well as the side length of a square given the length of the diagonal. This geometry video contains plenty of examples and practice problems. Polygons: https://www.youtube.com/watch?v=E_-3ulbtcLk Quadrilaterals: https://www.youtube.com/watch?v=ogcH3eM5beM Points, Lines, Planes, & Segments: https://www.youtube.com/watch?v=dDWjhRfBsKM Similar Triangles: https://www.youtube.com/watch?v=YiFwvAFk-xs Pythagorean Theorem: https://www.youtube.com/watch?v=d8EA5TxGzcY _________________________________ The Distance Formula: https://www.youtube.com/watch?v=YDvUy5VYm9E Distance Between 2 Points - 3D: https://www.youtube.com/watch?v=0c6cP2zLC2c Special Right Triangles - 30 60 90: https://www.youtube.com/watch?v=p70UBGCHZrQ Special Right Triangles - 45 45 90: https://www.youtube.com/watch?v=xzMirNSv1d0 Trigonometric Ratios: https://www.youtube.com/watch?v=9-eHMMpQC2k _________________________________ Angle of Elevation Word Problems: https://www.youtube.com/watch?v=uyKvSe6Ltgs Finding The Missing Side of a triangle: https://www.youtube.com/watch?v=tielQ3ejh70 Finding The Missing Angle of a Triangle: https://www.youtube.com/watch?v=4Dv5IFqATrc Two Triangle Trigonometry Problems: https://www.youtube.com/watch?v=OTP885mApV8 How To Find The Area of a Rectangle: https://www.youtube.com/watch?v=M8JdRHeQBW8 ________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections

• published: 29 Dec 2017
• views: 530987

34:00

Math's Fundamental Flaw

• Order: Reorder
• Duration: 34:00
• Uploaded Date: 22 May 2021
• views: 27915597

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is ...

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ References: Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013 Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019 Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006 Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010 Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995 Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931 Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910 Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986 Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Executive Producer: Derek Muller Writers: Adam Becker, Jonny Hyman, Derek Muller Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman SFX & Music: Jonny Hyman Camerapeople: Derek Muller, Raquel Nuno Editors: Derek Muller Producers: Petr Lebedev, Emily Zhang Additional video supplied by Getty Images Thumbnail by Geoff Barrett ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

https://wn.com/Math's_Fundamental_Flaw

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ References: Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013 Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019 Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006 Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010 Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995 Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931 Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910 Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986 Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Executive Producer: Derek Muller Writers: Adam Becker, Jonny Hyman, Derek Muller Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman SFX & Music: Jonny Hyman Camerapeople: Derek Muller, Raquel Nuno Editors: Derek Muller Producers: Petr Lebedev, Emily Zhang Additional video supplied by Getty Images Thumbnail by Geoff Barrett ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

• published: 22 May 2021
• views: 27915597

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15:11

Bayes theorem, the geometry of changing beliefs

Perhaps the most important formula in probability. Help fund future projects: https://www....

published: 22 Dec 2019

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Bayes theorem, the geometry of changing beliefs

Bayes theorem, the geometry of changing beliefs

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• published: 22 Dec 2019
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Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/bayes-thanks Home page: https://www.3blue1brown.com The quick proof: https://youtu.be/U_85TaXbeIo Interactive made by Reddit user Thoggalluth: https://nskobelevs.github.io/p5js/BayesTheorem/ The study with Steve: https://science.sciencemag.org/content/185/4157/1124 http://www.its.caltech.edu/~camerer/Ec101/JudgementUncertainty.pdf You can read more about Kahneman and Tversky's work in Thinking Fast and Slow, or in one of my favorite books, The Undoing Project. Contents: 0:00 - Intro example 4:09 - Generalizing as a formula 10:13 - Making probability intuitive 13:35 - Issues with the Steve example Thanks to these viewers for their contributions to translations Gujarati: Hitesh12358, Pragna1991 Hebrew: Omer Tuchfeld Italian: @crampaldo ------------------ These animations are largely made using manim, a scrappy open-source python library: https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown

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1:27

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI. Subscribe: http://bit.ly/subscribe...

published: 11 Mar 2013

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Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI

Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI

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Theorem (1968) - Pier Paolo Pasolini (Trailer) | BFI. Subscribe: http://bit.ly/subscribetotheBFI Pier Paolo Pasolini's playful satire, starring Terence Stamp at the peak of his beauty. In cinemas 12 April Book tickets: http://bit.ly/13P9ula Watch more on the BFI Player: http://player.bfi.org.uk/ Follow us on Twitter: https://twitter.com/BFI Like us on Facebook: https://www.facebook.com/BritishFilmInstitute Follow us on Google+: https://plus.google.com/+britishfilminstitute/

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4:39

An introduction to mathematical theorems - Scott Kennedy

View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical...

published: 10 Sep 2012

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An introduction to mathematical theorems - Scott Kennedy

An introduction to mathematical theorems - Scott Kennedy

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View full lesson here: http://ed.ted.com/lessons/scott-kennedy-how-to-prove-a-mathematical-theory Euclid of Alexandria revolutionized the way that mathematics is written, presented or thought about, and introduced the concept of mathematical proofs. Discover what it takes to move from a loose theory or idea to a universally convincing proof. Lesson by Scott Kennedy, animation by Karrot Animation.

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4:11

Everything About Circle Theorems - In 3 minutes!

This is a graphic, simple and memorable way to remember the difference from a chord or a t...

published: 20 May 2015

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Everything About Circle Theorems - In 3 minutes!

Everything About Circle Theorems - In 3 minutes!

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• published: 20 May 2015
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This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to understand it myself, once i got to grips with it i decided to help others who were also stuck.. so this video was created... This video includes Perpendicular bisectors of any chord the angles in a semi-circle, what happens when a tangent and a radius meet, Angles that are in the same segment and how different they are, the circumference subtended by the same arc, the meaning of subtended, lengths of two tangents and finally the angle between a tangent and a chord.. aka Alternate Segment Theorem. I re-uploaded this video because the last one had some glitches so here we are againn.... FOR THE QUESTION IF YOU ARE STUCK okay so angle A is 55degrees. this is because the whole isosceles triangle adds up to 180degrees, you now take 70degrees from this because the angle on the far right hand side is 70degrees. this leaves us with 110degrees and you divide it by two (due to it being isosceles triangle) so angle A is 55degrees. if you go to 1:07 this explains the next part on why there is a 90degree angle on top of angle B.  you take 55degrees from that 90degrees because part of the right angle overlaps the first isosceles triangle (on the right hand side) and we have previously worked out that, that angle is 55degrees, this leaves us with 35degrees. now times that 35 by 2 which gives you 70degrees, take that answer AWAY from 180degrees because as you can see angle D is within ANOTHER isosceles triangle which means all the angles within the triangle add up to 180degrees. because angle D is within that triangle, angle D and the angle at the bottom right of the Isosceles triangle will EQUAL to the same amount. now divide the 110degrees by 2 to give you 55degrees.

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5:20

The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathe...

published: 20 Jul 2021

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The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

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• published: 20 Jul 2021
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Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. -- Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission ---------------------------------------------- Support us on Patreon: http://bit.ly/TEDEdPatreon Check out our merch: http://bit.ly/TEDEDShop ---------------------------------------------- Connect With Us ---------------------------------------------- Sign up for our newsletter: http://bit.ly/TEDEdNewsletter Follow us on Facebook: http://bit.ly/TEDEdFacebook Find us on Twitter: http://bit.ly/TEDEdTwitter Peep us on Instagram: http://bit.ly/TEDEdInstagram ---------------------------------------------- Keep Learning ---------------------------------------------- View full lesson: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy Dig deeper with additional resources: https://ed.ted.com/lessons/the-paradox-at-the-heart-of-mathematics-godel-s-incompleteness-theorem-marcus-du-sautoy#digdeeper Animator's website: https://basaestudio.com ---------------------------------------------- Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.

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0:44

Pythagorean theorem water demo

Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

published: 14 Apr 2009

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Pythagorean theorem water demo

Pythagorean theorem water demo

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Wheel with liquid demonstrates the Pythagorean theorem at Brentwood.

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5:50

Puscifer - "Theorem" (Official Video)

Puscifer’s video for “Theorem,” from the album “Existential Reckoning” Listen to Puscifer...

published: 02 Nov 2020

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Puscifer - "Theorem" (Official Video)

Puscifer - "Theorem" (Official Video)

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Puscifer’s video for “Theorem,” from the album “Existential Reckoning” Listen to Puscifer: Apple Music – https://music.apple.com/us/artist/puscifer/48261730 Spotify – https://open.spotify.com/artist/2pAajGWerK3ghwToNWFENS?si=DSiEUvpBS86Nzj54L_Bhvg Amazon Music - https://www.amazon.com/music/player/artists/B000TE0AUC Tidal - https://tidal.com/browse/artist/65016 Sign-up for tour updates: https://bnds.us/6qsj7t Watch more Puscifer videos: https://www.youtube.com/@pusciferdotcom/videos Subscribe to Puscifer’s YouTube channel: https://www.youtube.com/@pusciferdotcom?sub_confirmation=1 Follow Puscifer: Website & Store: https://puscifer.com/ Facebook: https://www.facebook.com/PusciferMusic Twitter: https://twitter.com/puscifer Instagram: https://www.instagram.com/puscifer/ YouTube: https://www.youtube.com/@pusciferdotcom Lyrics: Old notions: traps by nature, holding sentry over, we, the rigid, the self suppressing. New notions: holes we dig too quickly into which we fall. Just impulsive postulations. Seek the Balance. Work the Science. Through diligence, moderate the middle. Resilient, social architectures must be built upon arbitrated firm foundations. Integrating form & function, art & order, hope & proof, math & passion. Theorems old and new Seek the Balance. Work the Science. Be diligent. Moderate the middle. Synthesize. ©2020 Puscifer Entertainment under exclusive license to Alchemy Recordings, LLC / BMG Rights Management (US). FOLLOW ALCHEMY RECORDINGS https://www.facebook.com/AlchemyRecor... https://twitter.com/alchemyrecords https://www.instagram.com/alchemyreco... https://www.alchemyrecordings.com #Puscifer #Theorem #ExistentialReckoning

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8:48

What Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz

What Is Pythagoras Theorem? | Pythagoras Theorem Explained | Theorem For Kids | Maths For ...

published: 07 Aug 2020

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What Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz

What Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz

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• published: 07 Aug 2020
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What Is Pythagoras Theorem? | Pythagoras Theorem Explained | Theorem For Kids | Maths For Kids | Maths Theorem | Hypotenuse | Best Kids Show | Dr Binocs Show | Dr Binocs | Peekaboo Kidz Hey kids, in this video, Dr Binocs will explain, Why Is Pythagoras Theorem? | PYTHAGORAS THEOREM | The Dr Binocs Show | Peekaboo Kidz Make sure you watch the whole video to know all the answers to your curious questions! Leave your ideas, suggestions and questions for Dr. Binocs at this Email Id: [email protected] For more fun learning videos SUBSCRIBE to Peekaboo Kidz: http://bit.ly/SubscribeTo-Peekabookidz Watch Guess The Shapes With Baby Binocs here - https://youtu.be/vNm422Ta44w Watch other fun learning episodes of Dr. Binocs here - http://bit.ly/2kfNS22 Watch our NEW SERIES of Baby Binocs, stay tuned to this playlist - http://bit.ly/2kyC2jU Credits - Voice of Dr. Binocs & Kitty - Joseph D'Souza Creative Head/Director - Nitin Navale Writer - Nitin Navale Illustrators - Kalpesh Bamne, Mukesh Ishi Storyboard - Kalpesh Bamne Animators - Sushant Hodage, Tushar Ishi , Raju Nikumbe, Prashant Bordekar Co-ordinator- Aliasgar Kagalwala VFX Artist - Tushar Ishi Original Background Score & SFX - Varad J. Khare Sound Design: Varad J. Khare Sound Engineer - Varad J. Khare Producer - Neha Barjatya Copyrights and Publishing: Rajshri Entertainment Private Limited All rights reserved. #WhatIsPythagorasTheorem #PythagorasTheorem #DrBinocsShow #PeekabooKidz Catch Dr.Binocs At - https://goo.gl/SXhLmc To Watch More Popular Nursery Rhymes Go To - https://goo.gl/CV0Xoo To Watch Alphabet Rhymes Go To - https://goo.gl/qmIRLv To Watch Compilations Go To - https://goo.gl/nW3kw9 Catch More Lyricals At - https://goo.gl/A7kEmO Subscribe to Peekaboo Kidz: http://bit.ly/peekabookidz Like our Facebook page: https://www.facebook.com/peekabootv

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11:04

Pythagorean Theorem

This geometry video tutorial provides a basic introduction into the pythagorean theorem. ...

published: 29 Dec 2017

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Pythagorean Theorem

Pythagorean Theorem

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• published: 29 Dec 2017
• views: 530987

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhombuses, and trapezoids. This video explains how to calculate the perimeter of a rhombus and the area of a trapezoid using the pythagorean theorem as well as the side length of a square given the length of the diagonal. This geometry video contains plenty of examples and practice problems. Polygons: https://www.youtube.com/watch?v=E_-3ulbtcLk Quadrilaterals: https://www.youtube.com/watch?v=ogcH3eM5beM Points, Lines, Planes, & Segments: https://www.youtube.com/watch?v=dDWjhRfBsKM Similar Triangles: https://www.youtube.com/watch?v=YiFwvAFk-xs Pythagorean Theorem: https://www.youtube.com/watch?v=d8EA5TxGzcY _________________________________ The Distance Formula: https://www.youtube.com/watch?v=YDvUy5VYm9E Distance Between 2 Points - 3D: https://www.youtube.com/watch?v=0c6cP2zLC2c Special Right Triangles - 30 60 90: https://www.youtube.com/watch?v=p70UBGCHZrQ Special Right Triangles - 45 45 90: https://www.youtube.com/watch?v=xzMirNSv1d0 Trigonometric Ratios: https://www.youtube.com/watch?v=9-eHMMpQC2k _________________________________ Angle of Elevation Word Problems: https://www.youtube.com/watch?v=uyKvSe6Ltgs Finding The Missing Side of a triangle: https://www.youtube.com/watch?v=tielQ3ejh70 Finding The Missing Angle of a Triangle: https://www.youtube.com/watch?v=4Dv5IFqATrc Two Triangle Trigonometry Problems: https://www.youtube.com/watch?v=OTP885mApV8 How To Find The Area of a Rectangle: https://www.youtube.com/watch?v=M8JdRHeQBW8 ________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections

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Math's Fundamental Flaw

Not everything that is true can be proven. This discovery transformed infinity, changed th...

published: 22 May 2021

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Math's Fundamental Flaw

Math's Fundamental Flaw

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• published: 22 May 2021
• views: 27915597

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ References: Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — https://ve42.co/Dunham2013 Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — https://ve42.co/Conway1970 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — https://ve42.co/Churchill2019 Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — https://ve42.co/Gaifman2006 Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — https://ve42.co/Lnrt2010 Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — https://ve42.co/Poincare Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — https://ve42.co/Irvine1995 Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — https://ve42.co/Godel1931 Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — https://ve42.co/Russel1910 Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — https://ve42.co/Godel1986 Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — https://ve42.co/Cubitt2015 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Executive Producer: Derek Muller Writers: Adam Becker, Jonny Hyman, Derek Muller Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman SFX & Music: Jonny Hyman Camerapeople: Derek Muller, Raquel Nuno Editors: Derek Muller Producers: Petr Lebedev, Emily Zhang Additional video supplied by Getty Images Thumbnail by Geoff Barrett ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

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Legendre's three-square theorem

In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers

if and only if n is not of the form for integers a and b.

The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as ) are

History

Pierre de Fermat gave a criterion for numbers of the form 3a+1 to be a sum of 3 squares essentially equivalent to Legendre's theorem, but did not provide a proof. N. Beguelin noticed in 1774 that every positive integer which is neither of the form 8n + 7, nor of the form 4n, is the sum of three squares, but did not provide a satisfactory proof. In 1796 Gauss proved his Eureka theorem that every positive integer n is the sum of 3 triangular numbers; this is trivially equivalent to the fact that 8n+3 is a sum of 3 squares. In 1797 or 1798 A.-M. Legendre obtained the first proof of his 3 square theorem. In 1813, A. L. Cauchy noted that Legendre's theorem is equivalent to the statement in the introduction above. Previously, in 1801, C. F. Gauss had obtained a more general result, containing Legendre theorem of 1797-8 as a corollary. In particular, Gauss counted the number of solutions of the expression of an integer as a sum of three squares, and this is a generalisation of yet another result of Legendre, whose proof is incomplete. This last fact appears to be the reason for later incorrect claims according to which Legendre's proof of the three-square theorem was defective and had to be completed by Gauss.

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This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Legendre's_three-square_theorem

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